Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

December 6, 2009

Cobordism and Topological Field Theories Week 4

Posted by Alexander Hoffnung

Welcome to week 4 of the cobordism and TFT seminar at UCR by Chris Carlson. The previous lecture was put up a few weeks ago here. Sorry for the long break, but the next few should be coming in a more timely manner. So keep an eye out. This week’s lecture introduces 22-dimensional topological quantum field theories and commutative Frobenius algebras.

Here is the new lecture. Thanks to Christopher Walker for preparing these notes and the great pictures. The next lecture will be an introduction to the interactions between quantum field theories and topology by John Huerta.

Posted at December 6, 2009 12:07 AM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/2124

6 Comments & 1 Trackback

Re: Cobordism and Topological Field Theories Week 4

Does the ‘snake lemma’ at the beginning have anything to do with the snake lemma that I know? If so, I don't see it.

Posted by: Toby Bartels on December 6, 2009 1:45 AM | Permalink | Reply to this

Re: Cobordism and Topological Field Theories Week 4

I think this is going to be one of those times when it is just a coincidence. Maybe someone else knows better?

Posted by: Alex Hoffnung on December 6, 2009 2:54 AM | Permalink | Reply to this
Read the post Cobordism and Topological Field Theories Week 5
Weblog: The n-Category Café
Excerpt: Week 5 of the cobordism and TFT seminar gives a short history of the interactions of quantum field theories and topology.
Tracked: December 7, 2009 5:47 AM

Re: Cobordism and Topological Field Theories Week 4

Alex is right. They both have a snake-like look to them, so they both get the same name. One of them should be renamed to the worm lemma.

Posted by: Chris Carlson on December 7, 2009 7:08 PM | Permalink | Reply to this

Re: Cobordism and Topological Field Theories Week 4

Well, there seems to be only one Google hit for “Worm Lemma”, and this is in reference to a guest post by Anton Geraschenko at the Secret Blogging Seminar (the first ever guest post, in fact). Luckily, Anton is actually discussing something called the “Salamander Lemma”.

This post is really nice, but worth reading even just for sentences such as this one:

If you don’t like diagram chases, it’s likely that you still won’t like them once you know the Salamander lemma. The salamanders chase the diagrams for you, but you still have to chase the salamanders.

Posted by: Alex Hoffnung on December 7, 2009 7:33 PM | Permalink | Reply to this

Re: Cobordism and Topological Field Theories Week 4

Quick question to Alex and/or Chris Carlson. Where in the literature is this picture called the “Snake Lemma”? Perhaps you mean “Snake Relation”? (For example, section 2.3.11 in Joachim Kock’s book.)

Posted by: Chris Rogers on December 7, 2009 9:33 PM | Permalink | Reply to this

Re: Cobordism and Topological Field Theories Week 4

Snake relation sounds like the right name. Thanks! I have actually not seen this as snake lemma before.

That should clear up any confusion between the two, but I can imagine the appearance of the word “snake” in two contexts may have prompted such a question here nonetheless.

Posted by: Alex Hoffnung on December 7, 2009 9:58 PM | Permalink | Reply to this

Post a New Comment